Summer Run Analysis

Data Background Information

Treatment Averaged Data

Data Headers and Sample Records
Sample_Number	Date.Time	Sedum.rubro	Sedum.acre	bare.substrate	rubro.vs.substrate	acre.vs.substrate	timestamp	hour	day
1	8/2/19 14:55	26.67	26.50	26.83	-0.17	-0.33	2019-08-02 14:55:00	14	2019-08-02
2	8/2/19 15:25	24.67	24.67	24.83	-0.17	-0.17	2019-08-02 15:25:00	15	2019-08-02
3	8/2/19 15:55	39.33	41.00	42.00	-2.67	-1.00	2019-08-02 15:55:00	15	2019-08-02
4	8/2/19 16:25	34.17	33.00	34.67	-0.50	-1.67	2019-08-02 16:25:00	16	2019-08-02
5	8/2/19 16:55	35.50	33.00	35.17	0.33	-2.17	2019-08-02 16:55:00	16	2019-08-02
6	8/2/19 17:25	36.17	33.50	35.67	0.50	-2.17	2019-08-02 17:25:00	17	2019-08-02

Comparison of Treatment Avgerages

Table: Summary Statistics
comparison	mean(difference)	max(difference)	sd(difference)
rubro vs substrate	0.4203	6.67	0.943
acre vs substrate	-0.7841	3.83	0.889

Temperature Differences by Hour

Table: Difference Score Counts for Sedum rubrotinctum
counts	rubro - substrate	Percent (%) rubro
negative/colder	512	32.222
positive/hotter	836	52.612
zero/same	241	15.167

Table: Difference Score Counts for Sedum acre
counts	acre - substrate	Percent (%) acre
negative/colder	1393	87.670
positive/hotter	167	10.510
zero/same	29	1.825

Comparison of Temperatures by Hour

Daily Range, Max, and Min

Diurnal Temperature Ranges (DTR)

Table: Summary of Mean DTR for Each Treatment
mean(rubro_range)	mean(acre_range)	mean(soil_range)
18.5026	16.7153	17.8874

Daily Max Temperatures

Table: Summary of Maximum Temperature by Treatment
Category	rubro_max	acre_max
Lower Max (vs Soil)	1.000	34.000
Higher Max (vs Soil)	31.000	0.000
Same Max (vs Soil)	2.000	0.000
Average Max Temperature	36.706	34.377
Maximum Max Temperature	40.670	41.000

Daily Min Temperatures

Table: Summary of Minimum Temperature by Treatment
Category	rubro_max	acre_max
Lower Min (vs Soil)	19.000	34.000
Higher Min (vs Soil)	8.000	0.000
Same Min (vs Soil)	7.000	0.000
Average Min Temperature	18.203	17.662
Minimum Min Temperature	15.330	14.830

Paired T-Tests - DTR, Max, and Min

Table: Summary of Paired T-tests for DTR, Min, and Max Temperatures (alpha = 0.05)
t_test	p_value	CI_Lower	CI_Upper
rubro DTR	0.0000	0.3780	0.8526
acre DTR	0.0000	-1.3099	-1.0342
rubro max	0.0001	0.2714	0.7097
acre max	0.0000	-1.9654	-1.7105
rubro min	0.0023	-0.2017	-0.0478
acre min	0.0000	-0.7297	-0.6021

Linear Models for Treatment vs Control

Linear Model Summary Statistics: soil ~ Sedum rubrotinctum
term	estimate	std.error	statistic	p.value
(Intercept)	0.9763	0.0809	12.0659	0
Sedum.rubro	0.9457	0.0030	311.9704	0

Linear Model Summary Statistics: soil ~ Sedum acre
term	estimate	std.error	statistic	p.value
(Intercept)	-0.1425	0.0839	-1.6983	0.0896
Sedum.acre	1.0378	0.0033	313.7521	0.0000

Linear Model Summary Statistics
term	estimate	std.error	statistic	p.value
(Intercept)	24.4233	0.1783	136.9456	0
rubro.vs.substrate	2.0994	0.1728	12.1499	0

Linear Model Summary Statistics
term	estimate	std.error	statistic	p.value
(Intercept)	22.9475	0.2087	109.9427	0
acre.vs.substrate	-3.0077	0.1761	-17.0777	0

Appendix - Code

#setup and cleaning data

library("tidyverse")
library("scales")
library("MASS")
library("viridis")
library("DT")
library("rcompanion")
library("ggpubr")
library("car")
library("e1071") 
library("gridExtra")
library("reshape2")
library("lubridate")

setwd("/Users/edenaxelrad/Desktop/Green Roofs (Thesis)/Summer Run")

treat_avg <- read.csv("Interior Avgs.csv", stringsAsFactors = FALSE)
treat_avg$timestamp <- mdy_hm(treat_avg$Date.Time)
treat_avg$hour <- hour(treat_avg$timestamp)
treat_avg$day <- date(treat_avg$timestamp)
#Background information for treatment averaged data

head <- head(treat_avg)
knitr::kable(head, caption = "Data Headers and Sample Records")

rubro <- cbind.data.frame(treat_avg$timestamp, treat_avg$Sedum.rubro, "Sedum rubrotinctum")
colnames(rubro) <- c("Date", "Temperature", "Treatment")
acre <- cbind.data.frame(treat_avg$timestamp, treat_avg$Sedum.acre, "Sedum acre")
colnames(acre) <- c("Date", "Temperature", "Treatment")
soil <- cbind.data.frame(treat_avg$timestamp, treat_avg$bare.substrate, "Bare substrate")
colnames(soil) <- c("Date", "Temperature", "Treatment")

treat_temps <- rbind.data.frame(rubro, acre, soil)

ggplot(treat_temps, aes(Date, Temperature, color = Treatment)) + 
  geom_path() + facet_grid(Treatment ~ .) + 
  theme(legend.position = "none") + 
  ggtitle("Temperature by Treatment")

# Comparison of Treatment Avg at Samples

rubro <- cbind(treat_avg$rubro.vs.substrate, "rubro vs substrate")
colnames(rubro) <- c("difference", "comparison")

acre <- cbind(treat_avg$acre.vs.substrate, "acre vs substrate")
colnames(acre) <- c("difference", "comparison")

plot(treat_avg$Sample_Number, treat_avg$rubro.vs.substrate, type = "l",
     main = "(a) sedum rubrotinctum - bare substrate",
     xlab = "sample number",
     ylab = "temperature difference (C)")
abline(h=0, col="blue")
abline(h=mean(treat_avg$rubro.vs.substrate), col="red", lty = 2)

plot(treat_avg$Sample_Number, treat_avg$acre.vs.substrate, type = "l",
     main = "(b) sedum acre - bare substrate",
     xlab = "sample number",
     ylab = "temperature difference (C)")
abline(h=0, col="blue")
abline(h=mean(treat_avg$acre.vs.substrate), col="red", lty = 2)

long_data <- rbind.data.frame(rubro, acre)

long_data$difference <- as.numeric(as.character(long_data$difference))
long_data$abs_diff <- lapply(long_data$difference, abs)

summ_stats <-
  long_data %>%
  group_by(comparison) %>%
  summarize(mean(difference), max(difference), sd(difference))

knitr::kable(summ_stats, digits = 4, caption = "Table: Summary Statistics")

# Temperature Differences by Hour

neg_counts <- c("negative/colder", sum(treat_avg$rubro.vs.substrate<0), sum(treat_avg$acre.vs.substrate<0))
pos_counts <- c("positive/hotter", sum(treat_avg$rubro.vs.substrate>0), sum(treat_avg$acre.vs.substrate>0))
zero_counts <- c("zero/same", sum(treat_avg$rubro.vs.substrate==0), sum(treat_avg$acre.vs.substrate==0))

diff_counts <- rbind.data.frame(neg_counts, pos_counts, zero_counts)
colnames(diff_counts) <- c("counts", "rubro - substrate", "acre - substrate")

diff_counts$`rubro - substrate` <- as.numeric(as.character(diff_counts$`rubro - substrate`))
diff_counts$`acre - substrate` <- as.numeric(as.character(diff_counts$`acre - substrate`))

diff_counts <- 
  diff_counts %>%
  mutate("Percent (%) rubro" = signif(100*(`rubro - substrate`/1589), digits=5)) %>%
  mutate("Percent (%) acre" = signif(100*(`acre - substrate`/1589), digits=4))

diff_countsR <- diff_counts[,c(1,2,4)]
diff_countsA <- diff_counts[,c(1,3,5)]

get_density <- function(x, y, ...) {
  dens <- MASS::kde2d(x, y, ...)
  ix <- findInterval(x, dens$x)
  iy <- findInterval(y, dens$y)
  ii <- cbind(ix, iy)
  return(dens$z[ii])
}

treat_avg$hour  <- as.numeric(treat_avg$hour)

treat_avg$densityR <- get_density(treat_avg$hour, treat_avg$rubro.vs.substrate, n=40)
treat_avg$densityA <- get_density(treat_avg$hour, treat_avg$acre.vs.substrate, n=40)

ggplot(treat_avg) + 
  geom_point(aes(treat_avg$hour, treat_avg$rubro.vs.substrate, size = treat_avg$densityR, 
                 color = abs(treat_avg$rubro.vs.substrate))) + 
  geom_hline(yintercept=0, color = "white", alpha = 0.9) +
  geom_smooth(aes(treat_avg$hour, treat_avg$rubro.vs.substrate), color = "darkblue", se = FALSE) +
  scale_color_continuous(low = "blue", high = "red") + 
  guides(color = FALSE, size = FALSE) +
  ylim(-3.5,7.5) + ggtitle("(a) Sedum rubro - Bare Substrate") + 
  ylab("Temperature Difference") + 
  xlab("Hour")

knitr::kable(diff_countsR, digits = 4, caption = "Table: Difference Score Counts for Sedum rubrotinctum")
ggplot(treat_avg) + 
  geom_point(aes(treat_avg$hour, treat_avg$acre.vs.substrate, size = treat_avg$densityA, 
                 color = abs(treat_avg$acre.vs.substrate))) + 
  geom_hline(yintercept=0, color = "white", alpha = 0.9) +
  geom_smooth(aes(treat_avg$hour, treat_avg$acre.vs.substrate), color = "darkblue", se = FALSE) +
  scale_color_continuous(low = "blue", high = "red") + 
  guides(color = FALSE, size = FALSE) +
  ylim(-3.5,7.5) + ggtitle("(b) Sedum acre - Bare Substrate") + 
  ylab("Temperature Difference") + 
  xlab("Hour")

knitr::kable(diff_countsA, digits = 4, caption = "Table: Difference Score Counts for Sedum acre")
# Comparison of Temperatures by Hour

hrly_avg <-
  treat_avg %>%
  group_by(hour) %>%
  summarize(mean(Sedum.rubro), mean(Sedum.acre), mean(bare.substrate))

hrly_avg <- hrly_avg[1:24,]
hrly_avg$rubro_diff <- hrly_avg$`mean(Sedum.rubro)`- hrly_avg$`mean(bare.substrate)`
hrly_avg$acre_diff <- hrly_avg$`mean(Sedum.acre)`- hrly_avg$`mean(bare.substrate)`
hrly_avg[,2:6] <- round(hrly_avg[,2:6], 2)

plot(hrly_avg$hour, hrly_avg$`mean(Sedum.acre)`, type = "l", col = "blue",
     main = "Hourly Temperature Averages",
     xlab = "hour",
     ylim = c(15,40),
     ylab = "avg temperature (C)")
lines(hrly_avg$hour, hrly_avg$`mean(bare.substrate)`, col="black")
lines(hrly_avg$hour, hrly_avg$`mean(Sedum.rubro)`, col="red")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

only_8am <- 
  treat_avg %>%
  filter(hour == "8" | hour == "08") %>%
  group_by(day) %>%
  summarize(mean(bare.substrate), mean(Sedum.rubro), mean(Sedum.acre))

plot(only_8am$day, only_8am$`mean(bare.substrate)`, type = "l", main = "Daily Temperatures at 8am", xlab = "", ylab = "Temperature (C)", ylim = c(10,25))
lines(only_8am$day, only_8am$`mean(Sedum.rubro)`, type = "l", col = "red")
lines(only_8am$day, only_8am$`mean(Sedum.acre)`, type = "l", col = "blue")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

only_daytime <- 
  treat_avg %>%
  filter(hour > "10") %>%
  filter(hour < "17") %>%
  group_by(day) %>%
  summarize(mean(bare.substrate), mean(Sedum.rubro), mean(Sedum.acre))

plot(only_daytime$day, only_daytime$`mean(bare.substrate)`, type = "l", main = "Daily Temperatures from 11am to 4pm", xlab = "", ylab = "Temperature (C)", ylim = c(25, 42))
lines(only_daytime$day, only_daytime$`mean(Sedum.rubro)`, type = "l", col = "red")
lines(only_daytime$day, only_daytime$`mean(Sedum.acre)`, type = "l", col = "blue")
legend("topleft", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

datatable(hrly_avg, class = 'cell-border stripe', options = list(pageLength = 24))
# Diurnal Temperature Ranges (DTR) 

daily_range <- 
  treat_avg %>%
  group_by(day) %>%
  summarize(max(Sedum.rubro), min(Sedum.rubro), mean(Sedum.rubro), max(Sedum.acre), min(Sedum.acre), mean(Sedum.acre), max(bare.substrate), min(bare.substrate), mean(bare.substrate))

daily_range <-
  daily_range %>%
  mutate(rubro_range = `max(Sedum.rubro)` - `min(Sedum.rubro)`) %>%
  mutate(acre_range = `max(Sedum.acre)` - `min(Sedum.acre)`) %>%
  mutate(soil_range = `max(bare.substrate)` - `min(bare.substrate)`) 

plot(daily_range$day, daily_range$rubro_range, type = "l", col = "red",
     main = "Daily Temperature Ranges (Interior Sensors)",
     xlab = "",
     ylab = "Temperature Range (C)",
     ylim = c(10,25))
lines(daily_range$day, daily_range$acre_range, col="blue", lty = 1)
lines(daily_range$day, daily_range$soil_range, col="black", lty = 1)
legend("top", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

DTR_summ <-
  daily_range %>%
  summarize(mean(rubro_range), mean(acre_range), mean(soil_range))

knitr::kable(DTR_summ, digits = 4, caption = "Table: Summary of Mean DTR for Each Treatment")


Count_types <- c("Smaller DTR", "Larger DTR", "Same DTR")
Rdtr_counts <- rbind(sum((daily_range$rubro_range - daily_range$soil_range) < 0), sum((daily_range$rubro_range - daily_range$soil_range) > 0), sum((daily_range$rubro_range - daily_range$soil_range) == 0))

Adtr_counts <- rbind(sum((daily_range$acre_range - daily_range$soil_range) < 0), sum((daily_range$acre_range - daily_range$soil_range) > 0), sum((daily_range$acre_range - daily_range$soil_range) == 0))

DTR_counts <- cbind.data.frame(Count_types, Rdtr_counts, Adtr_counts)
# Daily Max Temperatures 

plot(daily_range$day, daily_range$`max(Sedum.rubro)`, type = "l", col = "red",
     main = "Daily Max Temperature (Interior Sensors)",
     xlab = "",
     ylab = "Temperature (C)",
     ylim = c(30,42))
lines(daily_range$day, daily_range$`max(Sedum.acre)`, col="blue", lty = 1)
lines(daily_range$day, daily_range$`max(bare.substrate)`, col="black", lty = 1)
legend("top", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

Category <- c("Lower Max (vs Soil)", "Higher Max (vs Soil)", "Same Max (vs Soil)", "Average Max Temperature", "Maximum Max Temperature")
rubro_max <- rbind(sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) < 0), 
                     sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) > 0), 
                     sum((daily_range$`max(Sedum.rubro)` - daily_range$`max(bare.substrate)`) == 0),
                     mean(daily_range$`max(Sedum.rubro)`),
                     max(daily_range$`max(Sedum.rubro)`))

acre_max <- rbind(sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) < 0), 
                     sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) > 0), 
                     sum((daily_range$`max(Sedum.acre)` - daily_range$`max(bare.substrate)`) == 0),
                     mean(daily_range$`max(Sedum.acre)`),
                     max(daily_range$`max(Sedum.acre)`))

Max_counts <- cbind.data.frame(Category, rubro_max, acre_max)
knitr::kable(Max_counts, digits = 3, caption = "Table: Summary of Maximum Temperature by Treatment")
# Daily Min Temperatures 

plot(daily_range$day, daily_range$`min(Sedum.rubro)`, type = "l", col = "red",
     main = "Daily Min Temperature (Interior Sensors)",
     xlab = "",
     ylab = "Temperature (C)",
     ylim = c(12,25))
lines(daily_range$day, daily_range$`min(Sedum.acre)`, col="blue", lty = 1)
lines(daily_range$day, daily_range$`min(bare.substrate)`, col="black", lty = 1)
legend("top", legend = c("substrate", "rubro", "acre"), col = c("black", "red", "blue"), lty=1:1, box.lty=0)

Category <- c("Lower Min (vs Soil)", "Higher Min (vs Soil)", "Same Min (vs Soil)", "Average Min Temperature", "Minimum Min Temperature")
rubro_max <- rbind(sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) < 0), 
                     sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) > 0), 
                     sum((daily_range$`min(Sedum.rubro)` - daily_range$`min(bare.substrate)`) == 0),
                     mean(daily_range$`min(Sedum.rubro)`),
                     min(daily_range$`min(Sedum.rubro)`))

acre_max <- rbind(sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) < 0), 
                     sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) > 0), 
                     sum((daily_range$`min(Sedum.acre)` - daily_range$`min(bare.substrate)`) == 0),
                     mean(daily_range$`min(Sedum.acre)`),
                     min(daily_range$`min(Sedum.acre)`))

Max_counts <- cbind.data.frame(Category, rubro_max, acre_max)
knitr::kable(Max_counts, digits = 3, caption = "Table: Summary of Minimum Temperature by Treatment")

t_test <- c("rubro DTR", "acre DTR", "rubro max", "acre max", "rubro min", "acre min")
p_value <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$p.value,
                  t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$p.value,
                  t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired = TRUE)$p.value,
                  t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired = TRUE)$p.value,
                  t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`, paired = TRUE)$p.value,
                  t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired = TRUE)$p.value)
CI_Lower <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$conf.int[1],
                  t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$conf.int[1],
                  t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[1],
                  t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[1],
                  t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`,paired=TRUE)$conf.int[1],
                  t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired=TRUE)$conf.int[1])

CI_Upper <- c(t.test(daily_range$rubro_range, daily_range$soil_range, paired = TRUE)$conf.int[2],
                  t.test(daily_range$acre_range, daily_range$soil_range, paired = TRUE)$conf.int[2],
                  t.test(daily_range$`max(Sedum.rubro)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[2],
                  t.test(daily_range$`max(Sedum.acre)`, daily_range$`max(bare.substrate)`, paired=TRUE)$conf.int[2],
                  t.test(daily_range$`min(Sedum.rubro)`, daily_range$`min(bare.substrate)`,paired=TRUE)$conf.int[2],
                  t.test(daily_range$`min(Sedum.acre)`, daily_range$`min(bare.substrate)`, paired=TRUE)$conf.int[2])


ttest_pvals <- cbind.data.frame(t_test, p_value, CI_Lower, CI_Upper)
knitr::kable(ttest_pvals, digits = 4, caption = "Table: Summary of Paired T-tests for DTR, Min, and Max Temperatures (alpha = 0.05)")
# Linear Models for Treatment vs Control

ggplot(treat_avg, aes(x=bare.substrate, y=Sedum.rubro)) + 
  geom_point()+
  geom_smooth(method = "lm")+
  ylim(10,43) + xlim(10,43) +
  ylab("sedum rubro")+
  xlab("bare substrate")+
  geom_abline(b=1, color="red", linetype=2)+
  ggtitle("(a) Linear Model of soil ~ Sedum rubrotinctum")


linearMod1 <- lm(bare.substrate ~ Sedum.rubro , data=treat_avg) %>%
  summary()%>%
  broom::tidy()

knitr::kable(linearMod1, digits = 4, caption = "Linear Model Summary Statistics: soil ~ Sedum rubrotinctum")
  
ggplot(treat_avg, aes(x=bare.substrate, y=Sedum.acre)) + 
  geom_point()+
  geom_smooth(method = "lm")+
  ylim(10,43) + xlim(10,43) +
  ylab("sedum acre")+
  xlab("bare substrate")+
  geom_abline(b=1, color="red", linetype=2)+
  ggtitle("(b) Linear Model of soil ~ Sedum acre")

linearMod2 <- lm(bare.substrate ~ Sedum.acre , data=treat_avg) %>%
  summary()%>%
  broom::tidy()

knitr::kable(linearMod2, digits = 4, caption = "Linear Model Summary Statistics: soil ~ Sedum acre")
ggplot(treat_avg, aes(x=bare.substrate, y=rubro.vs.substrate)) + 
  geom_point()+
  geom_smooth()+
  ylab("sedum rubro. - bare substrate")+
  xlab("bare substrate")+
  ggtitle("(a) Loess regression of soil ~ (Sedum rubrotinctum - soil)")

linearMod3 <- lm(bare.substrate ~ rubro.vs.substrate, data=treat_avg) %>%
  summary() %>%
  broom::tidy()

knitr::kable(linearMod3, digits = 4, caption = "Linear Model Summary Statistics")
ggplot(treat_avg, aes(x=bare.substrate, y=acre.vs.substrate)) + 
  geom_point()+
  geom_smooth()+
  ylab("sedum acre - bare substrate")+
  xlab("bare substrate")+
  ggtitle("(b) Loess regression of soil ~ (Sedum acre - soil)")

linearMod4 <- lm(bare.substrate ~ acre.vs.substrate, data=treat_avg) %>%
  summary() %>%
  broom::tidy()
knitr::kable(linearMod4, digits = 4, caption = "Linear Model Summary Statistics")
  
#looking at loess for daytime only - 10am to 7pm
daytime <- treat_avg %>%
  filter(hour > "10") %>%
  filter(hour < "19")

ggplot(daytime, aes(x=bare.substrate, y=acre.vs.substrate)) + 
  geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
  geom_point()+
  geom_smooth(method = "lm")+
  xlim(20,45) + ylim(-5,5) +
  ylab("sedum acre - bare substrate") +
  xlab("bare substrate") +
  ggtitle("LM of soil ~ (Sedum acre - soil) during the day time (10am to 7pm)")
# Appendix - Code

Summer Run Analysis

Eden Axelrad

9/4/2019

Summer Run Analysis

Data Background Information

Comparison of Treatment Avgerages

Temperature Differences by Hour

Comparison of Temperatures by Hour

Daily Range, Max, and Min

Diurnal Temperature Ranges (DTR)

Daily Max Temperatures

Daily Min Temperatures

Paired T-Tests - DTR, Max, and Min

Linear Models for Treatment vs Control

Appendix - Code